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Mathematical Problems in Engineering
Volume 2015, Article ID 319761, 13 pages
http://dx.doi.org/10.1155/2015/319761
Research Article

A Novel Dissipativity-Based Control for Inexact Nonlinearity Cancellation Problems

1Dipartimento di Ingegneria dell’Informazione, Università degli Studi di Firenze, Via S. Marta 3, 50139 Firenze, Italy
2School of Engineering, University of Liverpool, Liverpool L69 3GH, UK

Received 1 October 2014; Accepted 8 January 2015

Academic Editor: Victor Sreeram

Copyright © 2015 Giacomo Innocenti and Paolo Paoletti. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

When dealing with linear systems feedback interconnected with memoryless nonlinearities, a natural control strategy is making the overall dynamics linear at first and then designing a linear controller for the remaining linear dynamics. By canceling the original nonlinearity via a first feedback loop, global linearization can be achieved. However, when the controller is not capable of exactly canceling the nonlinearity, such control strategy may provide unsatisfactory performance or even induce instability. Here, the interplay between accuracy of nonlinearity approximation, quality of state estimation, and robustness of linear controller is investigated and explicit conditions for stability are derived. An alternative controller design based on such conditions is proposed and its effectiveness is compared with standard methods on a benchmark system.